Find the magnitude and position , Mechanical Engineering

Q1. A short vertical column consists of a channel section with the dimensions shown in Figure 1(a). The column (part of a system used to support a machine) carries a compressive point load of 40 kN at the corner of a plate welded to the top of the column (Figure 1(b)). The material from which the column is manufactured has an allowable maximum working stress of 200 MNm-2.

You are required to verify the structural integrity of the column. Your answer is required to be in the form of a short report giving your opinion of the suitability of the channel section chosen. The report should include appropriate calculations and any recommendations for modifying the column and/or the loading arrangement.

Q2. A shaft carries three rotating masses A, B and C of magnitude 10 kg, 9 kg and 16 kg with their centres of mass 90 mm, 120 mm and 45 mm respectively from the axis of rotation. The distance between the planes of rotation of A and B is 0.8 m and between B and C is 1.7 m. The angular positions of the masses measured from A in the same direction are B 60 and C 135.

Find the magnitude and position of the masses required in planes L and M, situated midway between the planes A and B and the planes B and C respectively, in order to produce complete balance. The radius of rotation of the balance masses is 160 mm.